Novel order parameter to describe the critical behavior of Ising spin glass models

A novel order parameter $\Phi$ for spin glasses is defined based on topological criteria and with a clear physical interpretation. $\Phi$ is first investigated for well known magnetic systems and then applied to the Edwards-Anderson $\pm J$ model on a square lattice, comparing its properties with the usual $q$ order parameter. Finite size scaling procedures are performed. Results and analyses based on $\Phi$ confirm a zero temperature phase transition and allow to identify the low temperature phase. The advantages of $\Phi$ are brought out and its physical meaning is established.